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A car has a weight of 12,000 N. The coefficient of kinetic friction between its wheels and the wet highway is 0.5. The car is travelling at 20 ms-1 when brakes are applied. How far does the car travel before it comes to a complete stop? Take g = 10 ms2 . |
A crate of mass 20.0 kg is pulled by a force of 180 N, up an inclined plane which makes an angle of 30º with the horizon. The coefficient of kinetic friction between the plane and the crate is k = 0.225. If the crates starts from rest, calculate its speed after it has been pulled 15.0 m. Draw the free body diagram. |
A ball having a mass of 0.5 kg is moving towards the east with a speed of velocity 8.0 ms1 . After being hit by a bat it changes its direction and starts moving towards the north with a speed of 6.0 ms1 . If the time of impact is 0.1 s, calculate the average force acting on the ball. |
An insect of mass 20 g crawls from the centre to the outside edge of a rotating disc of mass 200g and radius 20 cm. The disk was initially rotating at 22.0 rads1 . What will be its final angular velocity? |
A particle of mass 10.0 kg, initially moving with a velocity of ms 1 5.0 collides elastically with a particle of mass 5.0 kg, initially moving with a velocity of 8.0ms . 1 What are the velocities of the two particles before and after the collision in the centre of mass frame of reference? |
The amplitude of oscillation of a simple harmonic oscillator is 40 cm. Show that its instantaneous kinetic energy is less than its average kinetic energy when the displacement is 30 cm. |
The quality factor of a sonometer wire is 3000. The wire vibrates at a frequency of 250 Hz. Calculate the time in which its amplitude will reduce to half of its initial value. |
A transverse wave travelling in the positive x-direction is given by y(x,t) 6 sin(8t .05x) cm , where x is in cm and t is in seconds. Calculate the velocity of the wave and the maximum particle velocity |
For a particle undergoing uniform circular motion, show that (i) the velocity of the particle is perpendicular to the position vector, and (ii) the acceleration of the particle is perpendicular to its velocity. |
A box of mass 10 kg is pulled by a mass-less rope with a force of 40 N. The rope makes an angle of 30 with the horizontal. Draw the free-body diagram showing all forces on the box. Determine the acceleration of the box if the coefficient of kinetic friction between the floor and the box is 0.2. Take 2 g 10 ms . |
A ball of mass 100 g strikes a wall with the speed 1 2.0 ms and bounces off the wall in the opposite direction with the same speed. Calculate the impulse of the ball. |
A child of mass 30 kg travels in a lift. Calculate the force exerted on the child by the floor of the lift when the lift moves (i) downward with an acceleration of 2 1.0 ms , (ii) upward with an acceleration of 2 1.0 ms . What is the weight of the child when the lift falls freely? Take 2 g 10 ms . |
A child of mass 30 kg travels in a lift. Calculate the force exerted on the child by the floor of the lift when the lift moves (i) downward with an acceleration of 2 1.0 ms , (ii) upward with an acceleration of 2 1.0 ms . What is the weight of the child when the lift falls freely? Take 2g 10 ms . |
A satellite of mass 200 kg is displaced by a distance of 2RE from a point on the Earth’s surface, where RE is the radius of the Earth. Calculate the work done on the satellite by the force of gravitation. Take the values of the constants in your calculation from the astrophysical data given in the course. |
A child of mass 30 kg slides from rest down a wooden pole by a distance of 3.0 m. Calculate the average force of friction acting on the child if her speed is 1 2.0 ms when she hits the ground. Take 2 g 10 ms . |
The average angular acceleration of a stone lodged in a rotating car wheel is 2 100 rads . What will the stone’s final angular speed be after 3.0 s, if it starts from rest? Also calculate its angular displacement during this time. |
A star having rotational inertia of 48 2 10 10 kgm is rotating at an angular speed of 2.0 revolutions per month about its axis. The only force on it is the force of gravitation. When its nuclear fuel is exhausted, it shrinks to a neutron star having rotational inertia of 48 2 6.0 10 kgm . Determine the angular speed of the neutron star in revolutions per month. |
A steel ball A collides elastically with another steel ball B (at rest initially) and the ball B is observed to move off at an angle with the initial direction of motion of A. The mass of B is five times that of A. Determine the direction in which A moves after collision and the speeds of the two balls. |
Derive an expression for the logarithmic decrement of a damped oscillator |
A block attached to a spring is made to oscillate with initial amplitude of 8.0 cm. After 2.2 minutes, the amplitude decreases to 5.0 cm. Calculate (i) the time when the amplitude becomes 2.0 cm, and (ii) the value of damping constant for this motion. |
A sound wave of frequency 300 Hz travels with speed 340ms1 along the negative x-direction. Each point of the medium moves up and down through a total distance of 5.0 mm. Determine the necessary parameters to represent the wave mathematically. |
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